A total derivative tells you how a quantity changes if another quantity changes, regardless on the kind of dependence of the first quantity on the second. But for a partial derivative, the second quantity should only appear explicitly in the expression giving the first quantity.
For example consider [itex] y(x(t),t)=2x(t)^2+bt^2 [/itex], we'll have:
[itex]
\frac{\partial y}{\partial t}=2bt \\
\frac{d y}{dt}=4x(t) \frac{dx(t)}{dt}+2bt
[/itex]